1. Field of the Invention
This invention relates to flow control device simulation. More specifically, the invention is a method of simulating the flow-through area of a pressure regulator based on a projected flow pressure downstream of the pressure regulator.
2. Description of the Related Art
Complex flow networks are frequently modeled so that fluid flow through such a network can be simulated. For example, nodes and branches can be used to model a flow network in a space that can be one, two, or three-dimensional. Nodes are positions within the flow network where fluid properties (e.g., pressure, density, etc.) are either known or calculated. Branches are portions of the flow network where flow conditions (e.g., geometry, flow rate, etc.) are known or calculated. One type of branch feature that requires modeling and simulation is a pressure regulator branch.
An actual pressure regulator is essentially a mechanical balance device. A feedback loop from the pressure regulator's output senses pressure downstream of the device. The sensed pressure is then used to drive the device's balance. When the sensed downstream pressure is less than a target pressure value, the balance is driven to increase the regulator's flow-through area. An increased flow-through area increases the flow rate into the downstream volume resulting in an increased sensed pressure. When sensed downstream pressure is greater than the target pressure value, the balance is driven to decrease the regulator's flow-through area. A decreased flow-through area decreases the flow rate to the downstream volume resulting in a decreased sensed pressure. If no flow rate is required, the flow-through area goes to zero once the sensed downstream volume is brought up to the target pressure value. If the sensed pressure never reaches the target pressure value, the flow-through area will eventually go to a user-specified maximum value. The rate at which a pressure regulator responds is a function of the downstream volume, the pressure difference between the target pressure value and the sensed pressure, and the stiffness of the balance.
An existing method for simulating a pressure regulator's flow-through area is based on a backwards-looking approach that uses the rate of area change in the recent past, a target regulation pressure, and a relaxation factor to determine the new flow-through area. The method is disclosed in detail in “Development of a Pressure Regulator Option for the Generalized Fluid System Simulation Program (GFSSP),” P. A. Schallhorn, Report No. MG-02-111, NASA MSFC Contract No. NAS8-00187, February 2002. Briefly, this method has an initial condition for flow-through area that is 50% of a user-specified maximum flow-through area. Further, this method zeroes the flow-through area when computed (downstream) pressure exceeds a target pressure. The disadvantages of this method include a false or forced start-up condition that leads to excessive start-up transients. The method also leads to numerically-unstable pressure regulation in highly transient systems due to area solutions that bounce around from zero to near convergence. However, neither of these situations is particularly demonstrative of the response of an actual pressure regulator.